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					  A NEW APPROACH TO LAGEOS SPIN ORIENTATION AND
   ITS ROLE IN GENERAL RELATIVITY MEASUREMENTS

                                    DOUGLAS CURRIE
Department of Physics, University of Maryland, College Park, MD, 20742, USA

SIMONE DELL’AGNELLO, GIOVANNI DELL MONACHE, ROBERTO TAURASO
        LARES-GRUPPO 2, INFN/LFN, via E. Fermi, 40, Frascati, Italy
    The two LAGEOS Satellites have addressed a variety of issues in Geophysics (GP) and
    General Relativity (GR). The extreme accuracy of laser ranging (currently approaching
    millimeter accuracy) now means that very small error sources act upon LAGEOS and
    have become important, affecting the study of GP (e.g., the tides) and GR (e.g., Lenses-
    Thirring Effect). Initial measurements and analysis of the spin orientation were first
    performed at the in the early 1990s at the University of Maryland. However, the spin rate
    of LAGEOS has slowed to the point that this method is no longer effective. A new
    observing approach (the “Pocket Modulation Effect”) to determine the spin axis has been
    proposed by the first author. Data that addresses this method has been collected at
    various sites and is being analyzed at LNF/INFI. We will report on the physics involved
    in the PME and describe the laboratory data and simulations performed to validate the
    proposed approach, the LAGEOS data obtained at sites, the new analysis procedures and
    then address the impact of this new information.


1. Science Motivation

1.1. M ach’s Principle and General Relativity (GR)
Mach’s Principle addresses the fact while we cannot distinguish the physics in
frames in relative linear motion, we can clearly distinguish a rotating frame.
Earnest Mach addressed this problem in 1893, and hypothesized that a “non-
rotating” frame was established by the distant matter in the universe, that is, the
distant matter of the universe affects the physics in a local frame. Within the
framework GR, such an effect may exist, related to the measurement of the so-
called Lense-Thirring effect.

1.2. Lense-Thirring Effect – (L-TE)
Many parameters of GR have been experimentally addressed. However, almost
all of these experiments address static effects, that is, the effects on experiments
of a static configuration of masses. The dynamical effects, that is, the effects of
the effects caused by moving masses has only recently been addressed. The L-
TE is the effect of the mass current of the rotating earth, i.e., as it twists space-
time and alters the orientation of a gyroscope. Using the LAGEOS satellite,
Ciufolini has evaluated the L-TE at the 10% level. GPB is another experiment
expected to address the measurement of the L-TE.



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1.3. Gravito-Electro-Magnetics
The L-TE can be understood by noting the close relationship between these
aspects of L-TE and the theory of Electrodynamics. Just as an electric current in
a closed loop generates a dipole magnetic field that causes a compass needle to
twist, the mass current generated by the rotation of a finite size spinning body
such as the earth and its rotation generates effects in L-TE that causes a twist in a
local frame outside the earth. This is the L-TE for a satellite such as LAGEOS.
Another effect that can be addressed with respect to the Gravito-Electro-
Dynamics approach as the interaction of two parallel currents.                     In
electrodynamics this is referred to as Ampere’s Law. The “mass currents”
generated by the motion of the earth and moon about the sun also cause an effect
on the moon’s orbit. This should be measurable with the new accuracy expected
with the APOLLO Lunar Ranging Station and the even higher accuracy of the
proposed new arrays for the moon proposed by the University of Maryland.

1.4. Chern-Simons Gravity
Within the structure of String Theory, Chern & Simons have proposed a
modification of the GR equations. It has recently been shown by Smith et. al.
that using the measurements of the L-TE with the LAGEOSs they can place
interesting limits on the magnitude of the coupling coefficients. This addresses
such recently discovered phenomena as Dark Energy.

2. Technology Aspects
We now address some technology aspects of the measurements using LAGEOS
and future similar satellites. We will review the methods of measurements and
then the possible error sources and finally the methods to correct these forces.
However, most of the material will be review very briefly and we shall
concentrate on the effects of photon thrust. That is, the emission of photons
from the heated surface of the satellite and the reaction that moves the satellite
into an new orbit.

2.1. Laser Ranging Accuracy
The orbits of the satellites are determined by laser ranging, using a very narrow
laser pulse is sent from a ground station, reflected directly back to the ground
stations by special mirrors, the Cube Corner Retro-reflectors, (CCRs). Photo-
detectors then receive the reflected pulse and determine the time since the
transmission. From such repeated measurements, one determines the orbit of the
satellite. Currently, for most of the interesting measurements, the limiting
accuracy is not the precision to which this time can be measured, but other more
systematic effects to be addressed in the next sub-sections.

2.2 Gravitational Forces
                                                                                      3


Of course the dominate “force” on the satellites is the gravitational force of the
earth, the “force” that assures the satellite moves on a geodesic from the view of
GR. The higher moments in the gravitational field must be known very
accurately in order to form a basic reference orbit. Recent satellite measurements
have reduced the gravitational field uncertainties to a level that is acceptable.

2.3. Non-Gravitational Forces
In addition to the gravitational forces, there are a number of non-gravitational
forces that must be addressed. These consist of solar pressure, atmospheric drag
due to both neutral particles and charged particles. Again, these are manageable.
However, the photon thrust or thermal thrust is a force that must be addressed in
order to make the accurate measurements of the perturbations that are of interest.

2.4. Satellite Motions
We now briefly review the rotational effects on LAGEOS. It is essentially a
metal ball rotating in the magnetic field of the earth so electrical currents are
generated within the satellite. The energy of these currents, which comes from
the rotational energy, is converted to heat, so the rotation rate of the satellite
slows. Further, the earth’s magnetic field acting on these currents twists the
orientation of the spin axis.

2.5. Photon Thrust
Photon Thrust is the effect caused by the combination of the solar heating of the
satellite and the rotation of the satellite. Thus as the sun heats the satellite on
one side, an excess of infra-red photons are emitted. However, this warm side is
rotated away from the sun and the direction of the reaction force now depends
upon the rotation of the satellite. A more detailed analysis shows that for a
rapidly rotation satellite, the force is along the axis of rotating. Thus is critical to
determine the orientation of the spin axis in order to make these corrections.

3. Determination of the Direction of the Photon Thrust

3.1. Background – Solar Glint Approach (SGA)
There is a cluster of theoretical estimates of the spin rate, the orientation of the
spin axis. However, the first determinations of the orientation based upon
observations were conducted in the 1990s at the University of Maryland. The
orientation of the spin axis has been determined by the observation of the sun
glints reflecting from the front surface of the CCRs. These photometric records
can be used to determine the orientation of the spin axis. Andres was the first
incorporate the measurements into an orbital determination program LOSSAM.
In recent years, other stations have been performing the photometry to contribute
to the improved orbit evaluated by Andres.
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3.2. Current Challenges
 After launch, the rapid rotation of LAGEOS I permitted the SGA to be used
very effectively. However, it now has a period of thousands of seconds and the
SGA is no longer a feasible approach. The reason for the difficulty with slow
rotation is that the reflected image of the sun is a narrow beam as it sweeps
across the earth. Unless the apparent axis of rotation (primarily changing due to
the geometry of the pass) remains within one degree for a quarter of a rotation
period, the SGA cannot effectively be used. Thus the combination of the narrow
beam of the solar reflection and the slow rational period causes the problem. For
this reason, a new method is required.

4. Pocket Effect Approach

4.1. Theoretical Pocket Effect Approach (PEA)
In order to understand the PEA, consider the LAGEOS satellites as a shiny ball
with no CCRs. Viewed in the sunlight, we see a small (a few millimeters) image
of the sun on the surface. As the ball rotates, the brightness of the image remains
the same, yielding a constant photometric signature. Now consider a shiny ball
that his many holes or pockets so much of the surface is covered with pockets.
Now as the shiny ball with pockets rotates, when the image of the sun is on the
remaining shiny surface, we again see the constant photometric signature.
However, as a hole rotates into the image of the sun, the intensity of the
reflection will go to zero. During the rotation, we expect to see no intensity for
about 8 degrees of rotation and the bright surface signature during abut 2 degrees
of rotation. Thus due to the larger angles of rotation covered by the PEA, one
has several hundred times better coverage for the rotation information. In fact,
since more than half of the surface is covered with pockets so we always get
signatures, unlike the SGA. Now consider a CCR in each of the pockets. If the
image of the sun passes very precisely over the center of the pocket, we will get
a Fresnel reflection and a very bright signal. However, this will happen only
occasionally for LAGEOS II and never twice for the same band for LAGEOS I
due to the latter’s slow rotation.

4.2. Experimental Laboratory Test
To confirm these theoretical expectations of the satellite behavior, we have
obtained a GSFC engineering model that was built with LAGEOS I. It is a
sector of the LAGEOS satellite that has been loaned to INFN for these tests. A
video taken as the sector rotates confirms the above expectations.

4.3. LAGEOS II observations
In 2004, LAGEOS II was observed on the 3.6 meter telescope at the Starfire
Optical Range in New Mexico, USA using the RULLI camera built by LANL.
This camera records the time of arrival of individual photoelectrons extreme
                                          RULLI Observations of LAGEOS II




                                   The upper plot displays the solar glints recorded by the RULLI Camera These
                                   solar glints have been used at the University of Maryland to determined the
                                   orientation of the spin axis. The lower curve illustrates the variation in the
                                   diffuse reflection. It is the latter we are now using to test the new method to
                                   determine the orientation.
                                                                                  5


precision. The figure shows a 600 second recording of the solar reflection of
LAGEOS II.

4.4. Data Reduction
The development of the analysis algorithms is in progress. This data will
initially be treated in the same manner as the SGA data. However the results are
obviously less accurate in the angle than the SGA. The PEA will predict and/or
identify when a SGA glint will occur. Thus with a single SGA glint, we can
identify its source and use it to the upgrade the accuracy to the SGA level.

6. Conclusions
The use of artificial and natural satellites has already yielded most of the most
accurate tests of GR. In the future, they should lead to a better understand of the
dynamical effects in GR, especially w.r.t. the L-TE, String theory in the Chern-
Simons approach and torsion effects. A critical aspect is to retain the ability to
measure the orientation of the spin axis of the LAGOES-type satellites during
the time that they are slowing. The PEA is providing such an observational and
analytic approach. An expanded version of this paper with figures, videos and
references may be found at http://www.physics.umd.edu/rgroups/astrometro.html
and at http://www.lnf.infn.it/acceleratori/lares/LAGEOS%20article%20list.htm

7. Acknowledgements
The author thanks David Thompson of LANL, Mark Davis of NRL and Ron
Dantowitz of the Clay Center Observatory for LAGEOS observations. The first
author also thanks INFN for travel support to coordinate the analysis of this data.

				
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posted:6/24/2011
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